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2015•Yingyong shuxue yu jisuan shuxue xuebaoRequires access

New choice of preconditioner of SOR-like method for saddle point problems

DI Jingjin

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Abstract

Golub,et al.studied an SOR-like iterative method with an auxiliary preconditioning parameter matrix for solving saddle point problems(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71-85).With a new choice of the auxiliary preconditioner,we accelerate the SOR-like method to solve such saddle point systems whose(1,1)block is a symmetric positive definite M-matrix.We compare it with the preconditioners proposed by Golub,et al.in numerical experiments and the results show that the new preconditioner outperforms the previous ones.

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What this paper is about

Golub,et al.studied an SOR-like iterative method with an auxiliary preconditioning parameter matrix for solving saddle point problems(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71-85).With a new choice of the auxiliary preconditioner,we accelerate the SOR-like method to solve such saddle point systems whose(1,1)block is a symmetric positive definite M-matrix.We compare it with the preconditioners proposed by Golub,et al.in numerical experiments and the results show that the new preconditioner outperforms the previous ones.

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Available abstract

Golub,et al.studied an SOR-like iterative method with an auxiliary preconditioning parameter matrix for solving saddle point problems(Golub G H,Wu X,Yuan J Y.SOR-like methods for augmented systems.BIT,2001,41(1):71-85).With a new choice of the auxiliary preconditioner,we accelerate the SOR-like method to solve such saddle point systems whose(1,1)block is a symmetric positive definite M-matrix.We compare it with the preconditioners proposed by Golub,et al.in numerical experiments and the results show that the new preconditioner outperforms the previous ones.

Key concepts: Preconditioner, Saddle point, Mathematics, Positive-definite matrix, Saddle, Matrix (chemical analysis), Block (permutation group theory), Applied mathematics

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